1. Field of the Invention
This invention is concerned with a method for statistically studying and editing seismic velocities, such as are used for stacking and migration processes as applied in geophysical exploration of the subsurface of the earth. Of interest is a compact display of the regional velocity gradient.
2. Discussion of Related Art
Stacking and migration of raw seismic data requires a knowledge of the propagation velocity (hereinafter referred to simply as "velocity") of an acoustic wavefield through subsurface earth formations. Usually the velocity is calculated directly from the seismic data using as arguments, the square of the reflection travel time, t, and the square of the source-receiver offset, x, whereat that travel time was measured. Any one of a number of well-known algorithms may be used for the calculations.
Customarily velocity analyses are calculated at regular spatial intervals throughout the survey area often associated with selected CMP (common mid point) gathers. A typical velocity analysis may be presented as a time/velocity plot. The velocity data are estimated from the seismic reflection trajectories which are often contaminated with noise. A velocity analysis presentation may take the form of contours of trace-to-trace coherence or in the form of semblance peaks having an amplitude proportional the goodness of the inter-trace correlation. Because of noise-generated artifacts, most velocity analyses require a modest amount of interpretation before determining which semblance or coherence maxima will be used to construct the velocity function representative of the data.
The velocities determined in the manner described above usually vary vertically as an increasing function of depth (time) and they may vary spatially as a function of offset and azimuth. In a relatively confined, local area with minimal structural dip angles, a single depth-varying average velocity function suffices for the migration process. For an extended regional survey, in the presence of a significant lateral velocity gradient and steep formation dips, a three-dimensional, depth and spatially-varying velocity must be considered. That process requires very expensive, complex computer data processing.
Various approximate methods have been devised for economical data-migration in the presence of a significant lateral velocity gradient. One very successful technique makes use of a residual migration process. The basis of that technique involves migrating the data during a first pass using a constant minimal migration velocity. That step is followed by a second migration pass wherein a small residual migration is applied to the migrated seismic data from the first pass. The second-pass migration is calculated using; as an argument, the difference between the minimal migration velocity for the area and the local velocity existing at the grid position of the effective incident point of the data.
One such method is taught by U.S. patent application Ser. No. 07/739,140, now U.S. Pat. No. 5,233,569, issued Aug. 3, 1993 to C. Beasley et al. and assigned to the assignee of this invention, entitled MODIFIED RESIDUAL MIGRATION OF SEISMIC DATA, which is incorporated herein by reference with respect to the concept of residual migration velocities. Another relevant patent is U.S. Pat. No. 5,097,452, issued Mar. 13, 1992 to C. Beasley and assigned to the assignee of this invention, entitled ANALYSIS OF MIGRATION VELOCITY BY MIGRATION OF VELOCITY SPECTRA.
In the conduct of a large 2-D or 3-D geophysical survey, it is convenient to display a quantitative summary of the velocity gradient across an area of survey. The display would be constructed using statistical methods to filter out random velocity artifacts. One way would be to provide a contour map of some parameter that is a measure of the lateral velocity changes. One such method is disclosed in REGIONAL VELOCITY GRADIENT FROM NORMAL MOVEOUTS, Geophysics, v. 29, n. 6,December, 1964. That method of display is disadvantaged in that it is only two-dimensional in lateral space. The spatial velocity gradient is shown but not the vertical distribution. A separate map must be provided to show the velocity-field characteristics at each depth level of interest. Accordingly, it is somewhat awkward and bulky for routine use where a large area and many depth levels are under study.
There is a need for the provision of a single compact two-dimensional collective display of the statistical distribution of the velocity field characteristics within an extended region including both the temporal and spatial axes of the velocity field and for a method for determining an areal minimal migration velocity function for use in the earlier-referenced residual migration processes.